Aula 2- Definir e produzir gráficos de funções no Wolfram Mathematica

Introduction to Functions in Mathematics

Overview of the Lesson

• The session focuses on defining functions in mathematics, including how to create and plot them.

• The instructor discusses the interface of the mathematics software, emphasizing zooming features for better visibility.

Defining a Function

• To define a function, a name is assigned (e.g., F), followed by its variable (e.g., x).

• The correct syntax for defining a function includes using "colon equals" (:=) instead of just an equal sign.

• An example function f(x) = x^2 is defined, with optional parentheses for clarity.

Executing and Testing the Function

• After defining the function, it can be executed using Shift + Enter; this confirms that f(2) = 4 .

• Further testing shows that f(4) = 16 , validating the function's correctness.

Plotting Functions

Creating a Plot

• To plot the defined function f(x)=x^2 , use the command Plot with proper capitalization.

• The range for x values is specified from -4 to 4 when executing the plot command.

Customizing Graph Properties

• Additional customization options include labeling axes; Y-axis as f(x) , X-axis as x .

• Labels are enclosed in quotes to denote they are text rather than formulas.

Changing Graph Appearance

• Color customization is possible; users can specify colors like "Green" or "Darker Green" for visual preference.

How to Create and Customize Graphs in Python

Adding Titles to Graphs

• To add a title to a graph, use the plot Label function. Ensure the title is enclosed in quotes for it to be recognized as text.

• If not enclosed in quotes, the system interprets it as a mathematical function (e.g., f(x) = x^2 ).

• Correctly formatting the title allows for customization; you can name it anything you prefer.

Plotting Multiple Graphs

• When plotting multiple graphs together, you can either combine them into one plot or create separate plots and display them simultaneously.

• The preferred method is often to define each plot separately and then merge them later for clarity.

Defining Functions for Plots

• A new function can be defined using syntax like g(x) = x. This allows for easy evaluation of specific values (e.g., g(3) returns 3).

• After defining functions, they can be plotted over specified ranges (e.g., from -4 to 4).

Combining Plots

• Assign each plot to a variable (e.g., p1 and p2) before combining them. This helps manage multiple plots effectively.

• Use the command show(p1, p2) with proper capitalization to display both graphs together.

Customizing Axes Ranges

• You can customize the axes by specifying their ranges within curly braces when calling the show function.